Answer
$a_n= -3 \times (-5)^{n-1}$
$a_{15}=-18,310, 546, 875$
$S_{15}=-15,258, 789, 063$
Work Step by Step
The general formula for the nth term of a geometric series is given by $a_n= a_1r^{n-1}$ ...(1)
The ratio of the successive terms is $r=-5$ .
Equation (1) gives: $a_n= a_1 \times (-5)^{n-1}=-3 \times (-5)^{n-1}$
Plugging in $n =15$, we have
$a_{15}=-3 \times (-5)^{14}=-18,310, 546, 875$
We know that $S_{n}=\dfrac{a_1(1-r^n)}{1-r}$
Now, $S_{15}=\dfrac{-3 \times (1-(-5)^{15})}{1-(-5)} =-15,258, 789, 063$
